Kepler’s Snowflake

Johannes Kepler (1571–1630) wrote some of the foundational works of modern astronomy. He was the first to prove, for example, that planets orbit the sun in ellipses, not perfect circles. His curiosity was far-ranging, and in 1609 he wrote a brief essay about, of all things, a snowflake. This essay, presented as “A New Year’s Gift” to his patron at court, has been newly translated and released in a gift edition by a small publisher this year.

Kepler’s question, “Why do all snowflakes have six corners?,” wouldn’t be answered until the development of X-ray crystallography in the twentieth century. Inconclusive though it may be from a purely scientific perspective, his essay has great historical value. It is full of surprising revelations about the workings of early modern science—above all, its underemphasized relationship to poetry and mysticism.

Kepler As Poet

Kepler’s thinking about snowflakes works by way of visual metaphor. Neruda never wrote an Ode to a snowflake—but how readily we can imagine him invoking, in that unwritten poem, la granada and la comena. Masterfully unexpected juxtapositions, these: two warm-weather comparisons for an ice crystal! Neruda would have done it purely by sensory intuition. It’s precisely these poetically charged connections—snowflake, pomegranate, beehive—that Kepler hits on in his found poem.

But there’s more than just Neruda here. You can find notes of court poetry, and of Donne’s love of paradox: he presents the treatise as a “New Year’s Gift,” then with a wink says he gives a mere snowflake, a nothing, a nix—punning on how nix means snowflake in Latin, but sounds like nothing (“nicht”) in German. Kepler’s Snowflake, like Donne’s Flea, becomes something much bigger than itself by the time he’s done talking. (Kepler isn’t the only astronomer-mathematician with a poet’s instincts: Omar Khayyam is famous for his Rubaiyat, quatrains he jotted down between spells in the observatory.)

Kepler’s treatise even eschews easy closure, like a contemporary avant-garde poem. Spoiler alert: he never actually explains why a snowflake has six corners. In fact, at one point in his speculations, he actually concedes that he may be building his next few ideas on poppycock.

I will pursue . . . this conjecture as far as possible, and not examine until later whether it is in fact true. Otherwise, the untimely discovery of a mistake could keep me from my undertaking. . . .

This is an absolutely Keatsian comfort with uncertainty. I find it poetic, too, that the booklet about snowflakes (1611) came after the Astronomia Nova (1609). After, that is, Kepler had calculated the elliptical orbits of the solar system. This “New Year’s Gift” marks a turning—a “volta,” to use poetry lingo—from the heavenly to the earthly, a poetic transition if ever there was one. Imagine: the tired astronomer, eyes bloodshot, fingers ink-stained (Kepler did all his own calculations), walks out on a Prague bridge and notices the snowflakes landing on him, his celestial mind quickened by this symmetry on his sleeve.

The Only Poetic Questions are Questions of Form

The editors of the book seem to have sensed this poetic quality. They have added, in an appendix, John Frederick Nims’s 1990 pattern poem of the same name, a multi-part riff on the text and on Kepler himself. Nims shapes his stanzas as six-cornered snowflakes, an asterisk at every point. This use of the asterisk is a masterstroke of ingenuity—asterisk is Latin for little star.

The astronomer’s Snowflake takes shape very seriously, too. He was fond of geometry—he is known for discovering two solids, to this day called “Kepler’s polyhedra,” whose sides are made entirely of equilateral triangles. Here, Kepler examines octahedrons, spheres, and hexagons, running “thought experiments” with them, stacking them, squeezing them together, in the hopes of deriving some insight into the snowflake’s structure.

Shape, form: it’s only fitting I mention, then, the external form of this book. It’s a small book, just bigger than the Apple Magic Trackpad by my wrist. The cover is glossy, done in winter colors: blue, white, gray; the paper is thick and high quality, the font is an easy-to-read variant of Garamond, and there are several pages of line drawings: necessary, in my opinion, to follow some of the geometry digressions.

Why am I praising the material construction of this book? Because I held it in my hand, and I parted it with my thumbs. And the pleasure I took in that, while living through the early-twenty-first-century rise of the e-book, is important to document. I suspect that thinking so much about snowflakes made me think of books themselves as snowflakes—physically beautiful, melting away.

Is It Boring?

Burton, in the The Anatomie of Melancholie, thought he was writing a text on medicine. He never imagined the theory of the Four Humours would evaporate, and only fantastic mouthfuls of his prose would hold the future’s interest. Galileo’s books are taught in Italian high schools as masterpieces of style. We know Aristotle from his students’ lecture notes; that is why he’s no good for pleasure reading. Aristotle’s finished works, lost to posterity, were actually dialogues, praised by Cicero for their literary style. We have far fewer examples of major scientists presenting their own ideas in accessible form. Stephen Hawking and Freeman Dyson come to mind. Many others write for each other, with “science reporters” and “popularizers” serving as intermediaries for the general reader. Books of popular science avoid literary flourishes; they are after clarity, not beauty. No gratuitous puns on Nothing, no quotes from Vergil’sGeorgics.

Kepler, luckily for the reader, came from an era that antedates the death of literary style in scientific writing. He also came from an era before jargon. You don’t have to familiarize yourself with a special vocabulary to understand what he’s saying. You do have to pay attention, though; the work may be poetic, but it’s a difficult poetry. (His works of astronomy are harder to follow: too much math.) What works in our favor is that he’s writing, not to a fellow scientist, but to his patron at court, the delightfully named Lord Wacker von Wackenfels.

Metaphor, Mother of Science

Late in the treatise, Kepler ponders snowflakes by pondering the frosty window above a hot bath. This is another visual metaphor, another example of poetic thinking. Metaphor, to a mind like his, is not a literary device or stylistic frill. The metaphor is the thought, not some ornament on that thought’s expression: the gift itself, not the bow on top. A law of physics doesn’t ornament the universe. It governs the universe.

Today’s scientists may roll their eyes at poetry, but they have kept their love—their need—for metaphor. The most useful metaphors of the modern era, after all, have come from scientists.

It’s not just that scientists rely on metaphor to describe things and processes they can’t directly observe (electron “cloud,” quantum “leap,” genetic “transcription”). Take it from a radiologist: the discipline of anatomy hides a visual metaphor under every pin.

Listen to the music of the spheres, and the ear bones involved are the stirrup, the anvil, and the hammer, which in turn bangs on the ear’s drum. We lose this sense of analogical—that is, poetic—thinking when we memorize stapes, incus, malleus, and tympanum. Metaphor was present at the very beginning of modern biology—and before the beginning as well. (This is why a daisy is the day’s eye, and a bluebell is exactly what it says it is.)

Scientific Latin is rarely as dry as it seems. A title like Sidereus Nuncius becomes a little less forbidding when you find out it means “Starry Messenger.” (Its author was the same Galileo who exclaimed, with high poetic anthropomorphism, that Saturn had “ears.”) Kepler, a contemporary of Galileo’s, played along, writing a response to Galileo’s work called Conversations with the Starry Messenger. Similarly, there is an interesting touch for the modern reader in the treatise’s title with its nive sexangula, “six-cornered snow.” That juxtaposition of the natural and the Latinate—“the Pedigree of Honey,” “an Amethyst remembrance,” “Inebriate of air”—is one of Emily Dickinson’s most alchemical effects. (“Inebriate,” either the verb or the participle, has never been used powerfully before or since, anywhere in English.)

Noticing those six corners, then contemplating, through a series of metaphors, why it should be so and not some other way: this is at once childlike wonder and grown-up investigation. It’s a mix that gives us the best science, and the best poetry.

The “Formative Faculty”

Kepler came from an earlier scientific culture when hard science wasn’t quite so hard. It hadn’t dissociated itself from theology or the humanities yet. Science considered itself one more way of marveling at the universe. Modern day atheists, in their bestselling polemics, tend to present science and religion as fighting a centuries-long duel. True, the Church was out to destroy Galileo—but Galileo was never out to destroy Christianity. This tends to be forgotten.

In the history of science, piety is more common than we would expect. The boom years (make that, boomcenturies) are full of reverent revolutionaries. Isaac Newton was religious to the point of wackiness; he spent years trying to decode the exact dimensions of Solomon’s Temple, which he believed could be found in the Hebrew of the Old Testament. The religious mind of Blaise Pascal has been preserved in hisPensees—a glowing book, yet one hears so rarely about it: a book that braids the rational and poetic in an eloquent double helix. Kepler himself studied theology at Tubingen. (An Introductory Essay in this edition opens with the surprising story of Kepler’s start as an astronomer: the University’s faculty assigned their student to teach astronomy at a provincial high school.)

These two things—the era’s indistinct boundary betwen science and religion, and an innate theological streak—lead to some truly unusual visions toward the middle and end of the book. Kepler, as it turns out, was not just a poet. He was also a mystic.

“That Thrice Greatest Animal, the Orb of the Earth”

Let me quote the whole passage where this startling phrase appears.

From this almost Nothing I have very nearly recreated the entire Universe, which contains everything! And having before shied away from discussing the tiny soul of the most diminutive animal, am I now to present the soul of that thrice greatest animal, the orb of the earth, in a tiny atom of snow?

Or as another mystical poet, William Blake, phrased it:

To see a World in a Grain of Sand
And a Heaven in a Wild Flower,
Hold Infinity in the palm of your hand
And Eternity in an hour.

That “Thrice Greatest,” by the way, may be a nod to Hermes Trismegistus, Thrice Great Hermes, founder of the “hermetic tradition” of alchemy, astrology, and magic. The connection isn’t idle speculation; Kepler’s mother was persecuted as a witch.

By calling the earth an animal, he incorporates the Latin word for “soul,” anima—Kepler is saying that the planet has a soul. He sounds like the Western World’s first environmentalist. Elsewhere the treatise speaks of the earth as a living thing, again, metaphorically. This time, the metaphor he selects is the human being: “There is thus a formative faculty in the body of the earth, and its vehicle is vapor, just as breath is the vehicle of the human soul. . . . ” This vapor condenses into snowflakes when its “constructive heat” meets the winter cold. Snowflakes are the earth’s breath on a cold day, rising as fog, falling as ice crystals.

For Kepler, symmetry is divine; a plant has symmetries because it has an anima, but this anima is dependent on the earth’s. Kepler’s metaphor is host-parasite: the planet is to its flora as “the human body [is] to lice.” Water vapor, the breath, was alive, just like the earth that breathed it. In Kepler’s time, remember, people believed in “lifesbreath,” the nishmath chayim (Hebrew, “breath of lives”) that God breathed into Adam. (They thought you could die if you sighed too deeply.) The snowflake’s sixfold symmetry arose because this seemingly inorganic thing was actually organic. Kepler couldn’t figure out why the snowflake had six corners—but he was certain, beforehand, that its symmetry was divine. “I believe that the cause behind the six-cornered snowflake is no other than the one responsible for the regular shapes and the constant numbers that appear in plants,” he writes. “I cannot believe that this ordered shape is present by chance.”

Centuries later, Einstein would echo this religious conviction. God does not play dice.

Fearsome Mystery, Fearsome Knowledge

As Nims writes in his poem, “Today, more knowing, we know less. But know / less more minutely. A schoolboy could / dazzle poor Kepler with his chemistry, / chat of molecular bonds, how H-O-H / freezes to crystal, the six struts / magnetized by six hydrogen nuclei.” X-ray crystallography has answered the question Kepler so brilliantly failed to answer. Physiology and Genetics have replaced “the formative faculty” with sodium-potassium ion pumps and deoxyribonucleic acid.

Does that mean that we can’t partake of Kepler’s reverent wonder, now that we know better than he did? Is there any point in reading a seventeenth-century treatise that didn’t answer what it set out to answer? I say yes. This is a great mind, dancing, and there is no such thing as a correct dance.

As for us, our modern wonder is of a different kind. Where the mystery has receded, the curiosity had flooded in. We revere by knowing, and we find the awe never needed the mystery. That has been the story of science for centuries now. The death of awe; the investigation; and finally the resurrection of awe, this time unkillable.

We experience that awe—not the mysterium tremendum but the scientia tremenda—when we see the Hubble telescope’s pictures of a dumbbell nebula, or an electron microscope’s snapshot of a dodecahedral virus. Kepler experienced both kinds of awe, too, the large-scale and the small-scale: once, when he looked to the heavens and realized the orbits were all ellipses; once when he looked to the earth and was charmed, as I have been, by The Six-Cornered Snowflake.